Handbook of Algebraic Topology

I.M. James0444817794, 9780444817792, 9780080532981

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

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Table of contents :
Front Cover……Page 1
Handbook of Algebraic Topology……Page 4
Copyright Page……Page 5
Contents……Page 8
Foreword……Page 6
List of Contributors……Page 10
Chapter 1. Homotopy types……Page 12
Chapter 2. Homotopy theories and model categories……Page 84
Chapter 3. Proper homotopy theory……Page 138
Chapter 4. Introduction to fibrewise homotopy theory……Page 180
Chapter 5. Coherent homotopy over a fixed space……Page 206
Chapter 6. Modem foundations for stable homotopy theory……Page 224
Chapter 7. Completions in algebra and topology……Page 266
Chapter 8. Equivariant stable homotopy theory……Page 288
Chapter 9. The stable homotopy theory of finite complexes……Page 336
Chapter 10. The EHP sequence and periodic homotopy……Page 408
Chapter 11. Introduction to nonconnective Im(J)-theory……Page 436
Chapter 12. Applications of nonconnective Im( J)-theory……Page 474
Chapter 13. Stable homotopy and iterated loop spaces……Page 516
Chapter 14. Stable operations in generalized cohomology……Page 596
Chapter 15. Unstable operations in generalized cohomology……Page 698
Chapter 16. Differential graded algebras in topology……Page 840
Chapter 17. Real and rational homotopy theory……Page 878
Chapter 18. Cohomology of groups……Page 928
Chapter 19. Homotopy theory of Lie groups……Page 962
Chapter 20. Computing v1-periodic homotopy groups of spheres and some compact Lie groups……Page 1004
Chapter 21. Classifying spaces of compact Lie groups and finite loop spaces……Page 1060
Chapter 22. H-spaces with finiteness conditions……Page 1106
Chapter 23. Co-H-spaces……Page 1154
Chapter 24. Fibration and product decompositions in nonstable homotopy theory……Page 1186
Chapter 25. Phantom maps……Page 1220
Chapter 26. Wall’s finiteness obstruction……Page 1270
Chapter 27. Lusternik-Schnirelmann category……Page 1304
Subject Index……Page 1322